What are the divisors of 8119?

1, 23, 353, 8119

There is a total of 4 positive divisors.
The sum of these divisors is 8496.
The arithmetic mean is 2124.

4 odd divisors

1, 23, 353, 8119

How to compute the divisors of 8119?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 8119 by each of the numbers from 1 to 8119 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

8119 / 1 = 8119 (the remainder is 0, so 1 is a divisor of 8119)
8119 / 2 = 4059.5 (the remainder is 1, so 2 is not a divisor of 8119)
8119 / 3 = 2706.3333333333 (the remainder is 1, so 3 is not a divisor of 8119)
...
8119 / 8118 = 1.00012318305 (the remainder is 1, so 8118 is not a divisor of 8119)
8119 / 8119 = 1 (the remainder is 0, so 8119 is a divisor of 8119)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 8119 (i.e. 90.105493728185). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

8119 / 1 = 8119 (the remainder is 0, so 1 and 8119 are divisors of 8119)
8119 / 2 = 4059.5 (the remainder is 1, so 2 is not a divisor of 8119)
8119 / 3 = 2706.3333333333 (the remainder is 1, so 3 is not a divisor of 8119)
...
8119 / 89 = 91.224719101124 (the remainder is 20, so 89 is not a divisor of 8119)
8119 / 90 = 90.211111111111 (the remainder is 19, so 90 is not a divisor of 8119)